6. High-performance computing in AZKIND

### 6.1. PARALUTION linear algebra library

HPC was implemented in AZKIND with the support of the linear algebra solvers library PARALUTION [13]. This open-source library is optimized for parallel computing process using graphics processing units (GPUs). For the numerical solution of an algebraic system A v!¼<sup>b</sup> ! PARALUTION includes numerical solvers to obtain the solution vector v ! for a known vector b ! and a specific matrix A that can be a symmetric or a non-symmetric matrix being also a sparse or a dense matrix. The working matrices in AZKIND are sparse non-symmetric matrices, and the bicgstab solver [14] was used for reactor simulations. The matrix solvers in PARALUTION are optimized to use on the non-zero (nnz) elements in the working matrices, saving processing time and computer memory.

### 6.2. Parallel processing for neutronic model

To demonstrate the HPC implementation in AZKIND, as described in Ref. [1], very large matrices were constructed for fine spatial discretization of arrangements of nuclear fuel assemblies of an LWR. Fine discretization means that each fuel assembly was subdivided in a mesh of size 10 10. As an example, an arrangement of 6 6 fuel assemblies consists of a square with 36 fine-discretized fuel assemblies. The corresponding algebraic system for each fuel arrangement was solved with parallel processing performed by the bicgstab solver mentioned earlier. In Tables 2 and 3, the speedup of the different cases is shown [1] with a remarkable performance. Despite the speedup for small matrices that is comparable for the three computer architectures used, it is also important to notice that the speedup values listed in Table 3 do not present a linear behavior, and the reason is because although more GPU processor cores are used with massive data transference to and from the GPU, a data traffic delay is present in the communication bus between the GPU and the CPU. For the analysis of the computing acceleration or "speedup," a definition of speedup is used in [15], known as relative speedup or speedup ratio: S = T1/Tn, where T1 is the computing time using a single processor (serial calculation) and Tn is the computing time using n processor cores. The "no memory" insert listed in Table 2 is because for those large matrix dimensions, there is not enough memory to load the matrix and solvers.

Figure 5 [1] shows the distribution of nuclear fuel assemblies in the core of a boiling water reactor. Excepting the blue-shaded zone, colors are for different types of fuel assemblies. In the plane xy, the mesh is 24 24, according to each fuel zone, and axially, there are 25 nodes. The matrix for this coarse mesh (1,274,304 nnz) is comparable to the matrix of the fine mesh created for the case of a unique assembly (case 1 1 listed in Table 2).

As described in [1], a reactor power transient was simulated as the capability to remove neutrons was highly increased in the perturbed assembly shown in Figure 5. An increase as


Table 2. Parallel processing time (seconds) in different architectures [1].


Table 3. Speedup comparison (S) [1].

6. High-performance computing in AZKIND

HPC was implemented in AZKIND with the support of the linear algebra solvers library PARALUTION [13]. This open-source library is optimized for parallel computing process using graphics processing units (GPUs). For the numerical solution of an algebraic system

a sparse or a dense matrix. The working matrices in AZKIND are sparse non-symmetric matrices, and the bicgstab solver [14] was used for reactor simulations. The matrix solvers in PARALUTION are optimized to use on the non-zero (nnz) elements in the working matrices,

To demonstrate the HPC implementation in AZKIND, as described in Ref. [1], very large matrices were constructed for fine spatial discretization of arrangements of nuclear fuel

and a specific matrix A that can be a symmetric or a non-symmetric matrix being also

! for a known

PARALUTION includes numerical solvers to obtain the solution vector v

6.1. PARALUTION linear algebra library

Figure 4. The NK-TH feedback process in AZKIND.

18 New Trends in Nuclear Science

saving processing time and computer memory.

6.2. Parallel processing for neutronic model

A v!¼<sup>b</sup> !

vector b !

7. Simulation of a reactor core condition

Figure 7. Axial power peaking profile location.

distribution resulted from the NK model running standalone.

A simple example was prepared to show the capability of the AZKIND code running with NK-TH coupling, and the thermal-hydraulic effect on power distribution is compared to the power

Nuclear Reactor Simulation

21

http://dx.doi.org/10.5772/intechopen.79723

This example was prepared for a two energy group, that is, fast neutrons and thermal neutrons. In LWR, the nuclear fissions of the fuel atoms are mainly coming from the thermal neutrons present in the reactor core. The effect observed in Figure 7 is that the TH feedback induces an increase in the thermal neutrons population and so increasing power. As the coolant/moderator enters the reactor core through the bottom part of the reactor and the core

Figure 5. A map of fuel assemblies in an LWR [1].

Figure 6. Simulation of a reactor power transient—serial and parallel processing.

step function in the neutrons removal capability during 3 s is implemented in the perturbed assembly, after that the perturbation finishes and the transient lasts for two more seconds, giving a reactor power reduction. The time step used in this simulation was 0.1 s. Figure 6 shows the power behavior over time, departing from a normalized value of 1.0 and reducing the power reactor to almost 80% of its original value. This reactor power transient was simulated with the AZKIND code, running on the three different GPUs listed in Tables 2 and 3. The right side of Figure 6 shows the time spent by AZKIND in a logarithmic scale, running in a sequential mode (Serial bar) and the times spent by each GPU card.
